3 Answers
3

Stalker

stalkern.stalk +‎ -er.
early 15c., "a poacher;" also "one who prowls for purposes of theft" (c.1500), agent noun from stalk (v.1).
A person who engages in stalking. Originally meant a tracker and hunter or guide of game. From Middle English stalken; from Old English -stealcian (as in OE bestealcian (“to move stealthily”)

Thus deerstalker (also deer-stalker) is an endocentric compound, the word deer describes what type of stalker (i.e. hunter) the person is. The name for ‘Sherlock Holmes hat’, a deerstalker, came later.

The earliest instance of the term deer stalker (without the hyphen) is found in 1818, The New Monthly Magazine, Volume 10.

... and absorbed in his own thoughts, he did not perceive a neighbour until spoken to by him. The bard reproached this intruder for coming upon him like the slow creeping deer stalker, and the intruder apologised, by assuring him, he had no intention of approaching as a spy; but he had lost his only pair of shoes and had nearly lost his life at sea.

This finding seems to precede OED's first recorded usage of 1830.

1830–35 D. Booth Analyt. Dict. Eng. Lang. 257 In the woodcraft of former times, many devices for catching deer were employed by the deer stalkers

In the 19th century, the pastime of hunting deer was considered a thrilling and noble pursuit, a definition of deer-stalking (British English) is provided by The Encyclopaedia Britannica, 1860, under the chapter ‘SHOOTING’.

The pursuit of deer with the rifle is termed deer-stalking. To kill the semi domesticated fallow deer requires little skill beyond that possessed by a good marksman. The skill of the deer-stalker, in pursuit of the red deer, is not only dependant on a good use of the rifle, but is shewn in his ability to find and approach deer; to do which successfully requires the most unwearied perseverance. Many of the Scottish forests wherein the stalking of deer in their wild state is practised, are of immense extent. It is on such tracts of land as the forests of Mar and Athole that the red deer is sought. [...] In these vast solitudes, the Highlander stalks the antlered monarchs of the herd, harts [adult male deer] which, a century ago, bore the scars of the weapons of his ancestors.

Unfortunately (for this user), there are no references concerning deer stalking clothes. But I did find one reference for deer-stalking hat, dated 1860, from a novel called "Plain Or Ringlets?" by Robert Smith Surtees

(page 316)
The first red coat he saw on the road set him on grinding his teeth, fretting and trying to be on—what he wanted was to be with the hounds. Even on the present occasion, when the Jug turned out in his old round-crowned deer-stalking hat, brown sea-side jacket and long leather gaiters, the horse felt by the hunting martingal on his shoulders what he was going to do.

(page 348) Sunday was a dies non at Appleton Hall, both in the eating, drinking and dressing way. There were neither sea-side coats, nor tweeds, nor deer-stalker hats, nor turbans with tassels, nor any of the complications of modern ingenuity to be seen; but, on the contrary, very sedate Sunday clothes of the plain orthodox order.

In an illustration on page 282, the hat worn by the gentleman carrying a rifle matches the description on page 316. There are no earflaps but it looks very similar to the tweed double-peak hat with which we're familiar.

The following source seems to confirm that the headwear called deerstalker was created around 1860, and it was therefore already well-known by 1870.

Caps made of tweed, with adjustable ear-flaps, were introduced in the eighteen-sixties for deer-stalking in the Scottish Highlands (hence the popular name “deerstalkers”) Hats: A History of Fashion in Headwear (1974)

As we might imagine, hunting clothes should be hardwearing, inconspicuous, and keep the huntsman warm and dry in all weather; but not at the expense of style and elegance, as shown in the following extracts, dated pre 1870:

(page 129)
Now in a fine tightly-fitting surtout, with a white vest and bloodstone buttons; next in a red-and-yellow-ribboned deer-stalker hat, with a tie to match ...

(page 234)
Mr. Romford, on the other hand, was the sportsman in mufti, deer-stalker hat, rough brownish Tweeds, and rusty Napoleons. Thus attired, they set out on their travels,

Napoleons were a 19th century boot reaching above the knee in front and with a piece cut out behind, they were originally worn by cavalrymen.

... and he wonders still more how he could dine without putting on the conventional white tie and black cloth; and the aspect of his deer-stalker, when compared with the pliant Gibus [a collapsible hat], is almost repulsive.

Another instance of deer-stalker hat, 1868, showing that this item of clothing was once considered fashionable and quite dapper.

... leaning against tree smiling-faced mesmeriser. Leslie's clothes were of a new cut, he was perfumed with musk, he wore a becoming deer-stalker hat, a handsome gold chain hung from his fob, he held a pair of kid gloves in his hands—his white fat hands; he looked fresh and comfortable, and perfectly easy in mind.

The first “deer-stalker's hats” looked quite different

I found a second source; Fraser's Magazine for Town and Country, Volume 4, 1831-1832, which confirms that the practice of placing a wing on the side of a deerstalker's hat was also performed in Scotland, thirty years earlier, with an eagle's wing no less.

(I'm going to presume that wing represented, or was idiomatic for feather.)

A later source, firmly establishes that it was customary for country hats to be decorated with a feather. The extract is from an article in the magazine called The Scottish Deer Forests, 1848.

How miserable is his stoop! how wretchedly he calculates his distance! That wideawake hat, which, for the sake of symmetry, he has been pleased to surmount with a feather, is as conspicuous to the country for miles round, and of course to the blackcock as white plume of Murat in the field of battle, and as potent to effect a clearance, ...

The widewake hat (or wide-awake) was a broad-brimmed, low-crowned hat made of soft felt, often worn by farmers. It was usually brown or black, but sometimes green.

A deerstalker is a type of hat that is typically worn in rural areas, often for hunting, especially deer stalking. Because of the hat's popular association with Sherlock Holmes, it is also a stereotypical hat of a detective.

It appears that a similar hat was formerly worn by hunters of deer, from which the name:

A close-fitting cap, usually woolen, such as is worn in deerstalking, having a low crown and visors both in front and back, and having earflaps which are usually worn tied together over the top; also called {fore-and-after}, {deerstalker hat} and {deerstalker cap}; a hunter's cap; formerly also used for any stiff, round hat.

[Webster]

Deerstalker:

noun Date: 1870 a close fitting hat with a visor at the front and the back and with earflaps that may be worn up or down called also deerstalker cap, deerstalker hat … (New Collegiate Dictionary)